Ko Jum
For a low-key island with local character, consider Ko Jum, where Long Beach (or Hat Yao) has plenty of space, and lovely sunsets over Ko Phi Phi.
You won't find large resorts with waterslides, but Long Beach has affordable family bungalows and swankier resorts towards the northern end, including one with various types of beach houses. Watch out for clusters of hidden rocks that kids can stub their toes on when wading.